Partial Decidable Presentations in Hyperarithmetic

[摘要] We study the problem of the existence of decidable and positive \(\Pi_1^1\)- and \(\Sigma_1^1\)-numberings of the families of \(\Pi_1^1\)- and \(\Sigma_1^1\)-cones with respect to inclusion. Some laws are found that reflect the presence of decidable computable \(\Pi_1^1\)- and \(\Sigma_1^1\)-numberings of these families in dependence on the analytical complexity of the set defining a cone.

[学科分类] 数学（综合）

[关键词] numbering;decidable numbering;positive numbering;computable numbering;computable set;computably enumerable set;e-reducibility;hyperarithmetic set;constructible admissible set